3.1168 \(\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^2} \, dx\)

Optimal. Leaf size=41 \[ -\frac{250 x^3}{27}+\frac{25 x^2}{54}+\frac{55 x}{9}+\frac{7}{243 (3 x+2)}+\frac{107}{243} \log (3 x+2) \]

[Out]

(55*x)/9 + (25*x^2)/54 - (250*x^3)/27 + 7/(243*(2 + 3*x)) + (107*Log[2 + 3*x])/2
43

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Rubi [A]  time = 0.0504428, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{250 x^3}{27}+\frac{25 x^2}{54}+\frac{55 x}{9}+\frac{7}{243 (3 x+2)}+\frac{107}{243} \log (3 x+2) \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^2,x]

[Out]

(55*x)/9 + (25*x^2)/54 - (250*x^3)/27 + 7/(243*(2 + 3*x)) + (107*Log[2 + 3*x])/2
43

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{250 x^{3}}{27} + \frac{107 \log{\left (3 x + 2 \right )}}{243} + \int \frac{55}{9}\, dx + \frac{25 \int x\, dx}{27} + \frac{7}{243 \left (3 x + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(3+5*x)**3/(2+3*x)**2,x)

[Out]

-250*x**3/27 + 107*log(3*x + 2)/243 + Integral(55/9, x) + 25*Integral(x, x)/27 +
7/(243*(3*x + 2))

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Mathematica [A]  time = 0.0174042, size = 44, normalized size = 1.07 \[ \frac{-40500 x^4-24975 x^3+28080 x^2+22740 x+642 (3 x+2) \log (3 x+2)+3322}{1458 (3 x+2)} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)*(3 + 5*x)^3)/(2 + 3*x)^2,x]

[Out]

(3322 + 22740*x + 28080*x^2 - 24975*x^3 - 40500*x^4 + 642*(2 + 3*x)*Log[2 + 3*x]
)/(1458*(2 + 3*x))

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Maple [A]  time = 0.009, size = 32, normalized size = 0.8 \[{\frac{55\,x}{9}}+{\frac{25\,{x}^{2}}{54}}-{\frac{250\,{x}^{3}}{27}}+{\frac{7}{486+729\,x}}+{\frac{107\,\ln \left ( 2+3\,x \right ) }{243}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(3+5*x)^3/(2+3*x)^2,x)

[Out]

55/9*x+25/54*x^2-250/27*x^3+7/243/(2+3*x)+107/243*ln(2+3*x)

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Maxima [A]  time = 1.332, size = 42, normalized size = 1.02 \[ -\frac{250}{27} \, x^{3} + \frac{25}{54} \, x^{2} + \frac{55}{9} \, x + \frac{7}{243 \,{\left (3 \, x + 2\right )}} + \frac{107}{243} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(2*x - 1)/(3*x + 2)^2,x, algorithm="maxima")

[Out]

-250/27*x^3 + 25/54*x^2 + 55/9*x + 7/243/(3*x + 2) + 107/243*log(3*x + 2)

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Fricas [A]  time = 0.223499, size = 57, normalized size = 1.39 \[ -\frac{13500 \, x^{4} + 8325 \, x^{3} - 9360 \, x^{2} - 214 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 5940 \, x - 14}{486 \,{\left (3 \, x + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(2*x - 1)/(3*x + 2)^2,x, algorithm="fricas")

[Out]

-1/486*(13500*x^4 + 8325*x^3 - 9360*x^2 - 214*(3*x + 2)*log(3*x + 2) - 5940*x -
14)/(3*x + 2)

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Sympy [A]  time = 0.211819, size = 34, normalized size = 0.83 \[ - \frac{250 x^{3}}{27} + \frac{25 x^{2}}{54} + \frac{55 x}{9} + \frac{107 \log{\left (3 x + 2 \right )}}{243} + \frac{7}{729 x + 486} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(3+5*x)**3/(2+3*x)**2,x)

[Out]

-250*x**3/27 + 25*x**2/54 + 55*x/9 + 107*log(3*x + 2)/243 + 7/(729*x + 486)

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GIAC/XCAS [A]  time = 0.210169, size = 77, normalized size = 1.88 \[ \frac{5}{1458} \,{\left (3 \, x + 2\right )}^{3}{\left (\frac{615}{3 \, x + 2} - \frac{666}{{\left (3 \, x + 2\right )}^{2}} - 100\right )} + \frac{7}{243 \,{\left (3 \, x + 2\right )}} - \frac{107}{243} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(2*x - 1)/(3*x + 2)^2,x, algorithm="giac")

[Out]

5/1458*(3*x + 2)^3*(615/(3*x + 2) - 666/(3*x + 2)^2 - 100) + 7/243/(3*x + 2) - 1
07/243*ln(1/3*abs(3*x + 2)/(3*x + 2)^2)